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Square matrix

from class:

Algebra and Trigonometry

Definition

A square matrix is a matrix with an equal number of rows and columns. It can be used in various mathematical operations, including solving systems of linear equations.

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5 Must Know Facts For Your Next Test

  1. A square matrix has dimensions n x n, where n is a positive integer.
  2. The determinant of a square matrix can be calculated and is crucial for solving systems of equations using Cramer's Rule.
  3. A square matrix can be symmetric if it equals its transpose (A = A^T).
  4. The identity matrix is a special type of square matrix with ones on the diagonal and zeros elsewhere.
  5. Invertible matrices are always square matrices, but not all square matrices are invertible.

Review Questions

  • What criteria must a matrix meet to be considered a square matrix?
  • How do you determine if a square matrix is invertible?
  • What role does the determinant play in solving systems of equations using Cramer's Rule?
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